Two antennas located at points A and B are broadcasting radio waves of frequency
ID: 1301191 • Letter: T
Question
Two antennas located at points A and B are broadcasting radio waves of frequency 95.0 MHz, perfectly in phase with each other. The two antennas are separated by a distance d=6.20m. An observer, P, is located on the x axis, a distance x=68.0m from antenna A, so that APB forms a right triangle with PB as hypotenuse. What is the phase difference between the waves arriving at P from antennas A and B?
The answer to this first part is .5612 rad. I only need help with the second part!
Now observer P walks along the x axis toward antenna A. What is P's distance from A when he first observes fully destructive interference between the two waves?
Explanation / Answer
Two antennas located at points A and B are broadcasting radio waves of frequency 82.0 MHz. The signals start in phase with each other. The two antennas are separated by a distance d = 8.0 m. An observer is located at point P on the x axis, a distance x = 100.0 m from antenna A. The points A P and B form a right triangle.
1)What is the phase difference between the waves arriving at P from antennas A and B? Enter your answer in radians (rad).
2)Now observer P walks along the x axis toward antenna A. What is P's distance from A when they first observe fully constructive interference between the two waves?
4pts
3)f observer P continues walking until they reach antenna A, at how many places along the x axis (including the place you found in the previous problem) will they find maxima in the radio signal due to constructive interference?
SOLUTION-
(1) ?=c/f , as c=3*10^8
?= 3*10^8/82*10^6= 3.6585m
PB= ?(8^2+100^2)= 100.3195
d= PB-PA= 0.3195m
3.6585:0.3195= 2?:x
x= 0.5487[rad]
(2) as LAP=x , LBP=y , n=1 , n?=3.6585m
y= x+3.6585 ----(1)
y= ?(x^2+8^2) ---(2)
(1)=(2)
x+3.6585= ?(x^2+8^2)
x^2+64= (x+3.6585)^2
x^2+64= x^2+7.317x+13.385
7.317x= 50.615
x= 6.9175= 6.92[m] approx
(3) n=2: n?=3.6585*2= 7.317m
x^2+64= (x+7.317)^2
x^2+64= x^2+14.634x+53.540
14.634x=10.460
x= 0.714796748= 0.715[m]